A teacher believing a student is more intelligent than they really are could change the interaction between this student and the teacher in many ways. This student could see the teacher having faith in them and perhaps seeing something in them that they don’t see in themselves. It could cause the student to have higher self esteem by this teacher thinking positively about them. This could be detrimental to the student because other students could consider the extra attention they’re getting from the teacher as favoring, in turn could cause other students to bully them accusing the student to be a teacher’s pet.

This theory is used in law enforcement with subjects that are have mental delirium or excessive excitability. If a subject is being hostile because they believe that crowd control is needed due to Elvis’ concert that’s about to begin, then law enforcement officers are able to “play along” with the subject in order to get them to do what needs to be done. This could be beneficial by the subject cooperating without anyone getting hurt, including them. This could be detrimental because if at any point the subject realizes what the law enforcement officer is doing, they may be under the impression that they’re being mocked or made fun of. This could easily cause the subject to become even more hostile than they were initially.

Works Cited

"Understanding the World Through the Thomas Theorem." Soul Shelter » Understanding the World Through the Thomas Theorem. N.p., n.d. Web. 22 Apr. 2013.

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...Historical Account:
Pythagoras, the namesake and supposed discoverer of the Pythagorean Theorem, was born on the Greek island of Samos in the early in the late 6th century. Not much is known about his early years of life, however, we do know that Pythagoras traveled through Egypt in the attempt to learn more about mathematics.
Besides his famous theorem, Pythagoras gained fame for founding a group, the Brotherhood of Pythagoreans, which was dedicated solely to study of mathematics and worship of numbers. Pythagoras passed on his belied that numbers are in fact the true "rulers of the universe".
While studying in Egypt, it is believed that Pythagoras studied with people known as the "rope-stretchers", the same people who engineered the pyramids. By using a special form of a rope tied in a circle with 12 evenly spaced knots, they discovered that if the rope was pegged to the ground in the dimensions of 3-4-5, the rope would create a right triangle. The rope stretchers used this principle to help accurately lay the foundations of for their buildings.
It was this fascination with the rope stretchers 3-4-5 triangle that ultimately led to the discovery of the Pythagorean theorem. While experimenting with this concept by drawing in the sand, Pythagoras found that if a square is drawn from each side of the 3-4-5 triangle, the area of the two smaller squares could be added together and equal the area of the large square....

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The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:[1]
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These two formulations show two fundamental aspects of this theorem: it is both a statement about areas and about lengths. Tobias Dantzig refers to these as areal and metric interpretations.[2][3] Some proofs of the theorem are based on one interpretation, some upon the other. Thus, Pythagoras' theorem stands with one foot in geometry and the other in algebra, a connection made clear originally byDescartes in his work La Géométrie, and extending today into other branches of mathematics.[4]
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...In mathematics, the Pythagorean theorem — or Pythagoras' theorem — is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). In terms of areas, it states:
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